Really, as you pointed out the only time they are supposed to is in order to get new converts, or out of necessity.
It is not permissible for a Muslim man or woman to take a male or female friend who is not a Muslim, because Allaah has forbidden us to love the kuffaar or take them as close friends and companions
It is permissible for you to let your aunt stay with you so that you can call her to Islam and encourage her with wisdom and beautiful preaching, If she sees you and your good attitude and kind treatment, that may be a means of opening her heart to this great religion. Attitude and actions may often be more eloquent than words and preaching. So strive hard to do that, and if Allaah guides her at your hands, that will be better for you than this world and everything in it.
In the Quraan, it says that we can not take the Kuffaar as awliyaa, but what does that mean? I mean, to what degree? Can we do business with them still? If I’m at school, can we play basketball with them? Can we talk to them about basketball and stuff? Can we hang out with them as long as they keep their beliefs to themselves? The reason I ask is because someone I know does hang out with them in this way and it doesn’t affect his beliefs, but I still tell him, “Why don’t you hang out with the muslims instead?” He says that most or many of the Muslims drink and take drugs where they hang out and they have girlfriends and he’s afraid that the sins of the Muslims will lure him, yet he’s sure that the Kufr of the Kaafirs will not lure him because that’s something that isn’t attractive to him. So is hanging out with them, playing sports with them, and talking with them about sports considered as “taking them as awliyaa instead of the believers” keeping in mind that he is doing that for his own eemaan?.
Praise be to Allaah.
Allaah has forbidden the believers to take the kaafireen (disbelievers) as friends, and He has issued a stern warning against doing that.
Here’s a site that sincerely believes all non-Muslims are condemned, so friendship requires the invitation to Islam.
Since you have feelings of concern for your friends, why don’t you give them Da’awah (invitation) to Islam. It is stated in the Hadith that ‘A true friend is he who invites his friend to the straight path, i.e. towards Islam, good deeds, charity, etc.’ Make lots of du’aa for your non-Muslim friends that Allah grant them the wealth of Imaan and that they realise the truth from falsehood.
Again the issue of being freinds for the purposes of conversion arises…
" Islam is the religion of tolerance, ease and flexibility, and at the same time, it is the religion of justice. Hospitality is a part of Islaamic good manners, but if the guest is a disbeliever, then the ruling differs according to the different intention of the host and the different types of hospitality he offers him. If his intention is legitimate, based upon his desire to create harmony between himself and the disbeliever, so that he may call him to Islaam and save him from kufr and misguidance, then his intention is honourable."
You’re not even considered a ‘brother’ of a Muslim
"Question: Does not brotherhood extend to all of mankind because it is established that Aadam was the forefather of everyone?
Response: This is not so. There is no doubt that everyone is from the offspring of Aadam but we do not say, “This is my brother,” when referring to a disbeliever meaning by that within the brotherhood of man. We can only refer to him as brother when there is a relationship by descent or lineage.
Although this deals with marriage, the implications of ‘mixing’ with non-Muslims still arises…
"Question: What is your advice concerning some Muslim minorities marrying disbelieving women who do not believe in the existence of a Creator and what is the effect of that upon the children?
Response: My advice to all Muslims is that they should not marry anyone who is not a Muslim.